Modeling and simulation of one- and two-row six-bladed ducted fans

The problem of simulation of efficient ducted fan type propulsors is considered. From experience of operation of twin blades in fantails of helicopters, it is known that this configuration creates less noise compared to a uniform arrangement of the blades around the circumference. However, the flow behind such fan is less uniform than that of a conventional ducted fan. For multicopter-type unmanned aircraft and air taxis, the key problem is flight in take-off and landing modes as well as acoustic and vortex fields created by propulsors in these modes. The decrease in the noise level in propellers with twin blades can potentially be accompanied by an increase in non-stationary vortex effects on the aircraft as well as a decrease in specific thrust. The objectives were to develop a method for simulation of ducted fan propellers in the takeoff and landing mode, to determine the optimal angle between the blades, and to compare a ducted fan with twin X-shaped blades to conventional blade position. Turbulent flows were calculated using transient Reynold-averaged Navier-Stokes equations, complemented by SST turbulence model, and large eddy simulation with WALE subgrid viscosity model. The calculations used the modification γ–Reθ Transition SST of the Langtry-Menter turbulence model, where there are relations for the intermittency criterion, which made it possible to consider the laminar-turbulent transition and the appearance of thin laminar separation bubbles that affect both the thrust of the propeller and the nonuniformity of the flow behind it. Testing was carried out on four-bladed propellers according to the known results of the TsAGI reference experiments. Testing of the γ–Reθ Transition SST Langtry-Menter turbulence model showed that it reproduces the dependence of the thrust coefficient and power factor on the blade angle better than the standard SST model. Calculations have shown that there is a clearly defined optimum angle between the paired blades. A comparison of three-bladed, six-bladed single and six-bladed propellers with twin blades showed that the latter option has slightly better thrust characteristics and creates a significantly lower noise level on the ground. The studied characteristics of ducted fans demonstrate the prospects for the use of propellers with twin blades in aircraft with vertical takeoff and landing. The developed numerical method can be directly used for industrial calculations of propellers and fans.

1. Chovancová A., Fico T., Chovanec L., Hubinský P. Mathematical modelling and parameter identification of quadrotor (a survey). Procedia Engineering, 2014, vol. 96, pp. 172–181. https://doi.org/10.1016/j.proeng.2014.12.139

2. Ostroukhov S.P. Aerodynamics of Aircraft Propellers and Annular Circular Propellers. Moscow, Fizmatlit, 2014, 328 p. (in Russian)

3. Buzikin O.G., Kazakov A.V., Shustov A.V. Numerical simulation of the aerodynamic performance of a micro air vehicle. TSAGI Science Journal. 2010, vol. 41, no. 5, pp. 535–550. https://doi.org/10.1615/TsAGISciJ.v41.i5.40

4. Nazarov D., Kondryakova A. Analisys of the flow past the screw with the use of numericaland experimental simulation. Izvestia of Samara Scientific Center of the Russian Academy of Sciences, 2018, vol. 20, no. 4-1, pp. 70–75. (in Russian)

5. Rumsey C.L., Biedron R., Farassat F., Spence P. Ducted-fan engine acoustic predictions using a Navier-Stokes code. Journal of Sound and Vibration, 1998, vol. 213, no. 4, pp. 643–664. https://doi.org/10.1006/jsvi.1998.1519

6. Reboul G., Polacsek C., Lewy S., Heib S. Aeroacoustic computation of ducted-fan broadband noise using LES data. Journal of the Acoustical Society of America, 2008, vol. 123, no. 5, pp. 3539. https://doi.org/10.1121/1.2934519

7. Myers L., Rhee W., Mclaughlin D. Aeroacoustics of vertical lift ducted rotors. Proc. of the 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), 2009, pp. 2009-3333. https://doi.org/10.2514/6.2009-3333

8. Astley R., Sugimoto R., Achunche I., Kewin M., Mustafi P., Deane E. A review of CAA for fan duct propagation and radiation, with application to liner optimization. Procedia Engineering, 2010, vol. 6, pp. 143–152. https://doi.org/10.1016/j.proeng.2010.09.016

9. Malgoezar A.M., Vieira A., Snellen M., Simons D.G., Veldhuis L.L. Experimental characterization of noise radiation from a ducted propeller of an unmanned aerial vehicle. International Journal of Aeroacoustics, 2019, vol. 18, no. 4-5, pp. 372–391 https://doi.org/10.1177/1475472X19852952

10. Zhang T., Barakos G.N. Review on ducted fans for compound rotorcraft. The Aeronautical Journal, 2020, vol. 124, no. 1277, pp. 941–974. https://doi.org/10.1017/aer.2019.164

11. Akturk A., Shavalikul A., Camci C. PIV measurements and computational study of a 5-inch ducted fan for V/STOL UAV applications. Proc. of the 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2009, pp. 2009-332. https://doi.org/10.2514/6.2009-332

12. Akturk A., Camci C. Experimental and computational assessment of a ducted-fan rotor flow model. Journal of Aircraft, 2012, vol. 49, no. 3, pp. 885–897. https://doi.org/10.2514/1.C031562

13. Yilmaz S., Erdem D., Kavsaoǧlu M. Effects of duct shape on a ducted propeller performance. Proc. of the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2013, pp. 2013–0803. https://doi.org/10.2514/6.2013-803

14. Akturk A., Camci C. Tip clearance investigation of a ducted fan used in VTOL unmanned aerial vehicles. Part I: Baseline experiments and computational validation. Journal of Turbomachinery, 2014, vol. 136, no. 2, pp. 021004. https://doi.org/10.1115/1.4023468

15. Xu H.-Y., Xing S.-L., Ye Z.-Y. Numerical study of ducted-fan lip stall suppression based on inflatable leading lip cell. Procedia Engineering, 2015, vol. 126, pp. 158–162. https://doi.org/10.1016/j.proeng.2015.11.202

16. Biava M., Barakos G.N. Optimisation of ducted propellers for hybrid air vehicles using high-fidelity CFD. The Aeronautical Journal, 2016, vol. 120, no. 1232, pp. 1632–1657. https://doi.org/10.1017/aer.2016.78

17. Chen J., Li L., Huang G., Xiang X. Numerical investigations of ducted fan aerodynamic performance with tip-jet. Aerospace Science and Technology, 2018, vol. 78, pp. 510–521. https://doi.org/10.1016/j.ast.2018.05.016

18. Ohanian O.J., Karni E.D., Londenberg W.K., Gelhausen P.A., Inman D.J. Ducted-fan force and moment control via steady and synthetic jets. Journal of Aircraft, 2011, vol. 48, no. 2, pp. 514–526. https://doi.org/10.2514/1.C031110

19. Mojzyh E.I., Zavalov O.A., Kuznetsov A.V. Experimental investigation of aerodynamic characteristics of unmanned aerial vehicle with lifted system of shrouded rotor. Trudy MAI, 2012, no. 50, pp. 11. (in Russian)

20. Dehaeze F., Barakos G.N. Hovering rotor computations using an aeroelastic blade model. The Aeronautical Journal, 2012, vol. 116, no. 1180, pp. 621–649. https://doi.org/10.1017/S0001924000007107

21. Abalakin I.V., Bakhvalov P.A., Bobkov V.G., Kozubskaya T.K., Anikin V.A Numerical simulation of aerodynamic and acoustic characteristics of rotor in ring. Matematicheskoe modelirovanie, 2015, vol. 27, no. 10, pp. 125–144. (in Rusian)

22. Abalakin I.V., Anikin V.A., Bakhvalov P.A., Bobkov V.G., Kozubskaya T.K., Numerical investigation of the aerodynamic and acoustical properties of a shrouded rotor. Fluid Dynamics, 2016, vol. 51, no. 3, pp. 419–433. https://doi.org/10.1134/S0015462816030145

23. Dehaeze F., Barakos G.N., Kusyumov A.N., Kusyumov S.A., Mikhailov S.A. Exploring the detached-eddy simulation for main rotor flows. Russian Aeronautics, 2018, vol. 61, no. 1, pp. 37–44. https://doi.org/10.3103/S1068799818010063

24. Golovkin M.A., Kochish S.I., Kritsky B.S. Calculation procedure of aerodynamic characteristics of the combined carrying system of the aircraft. Trudy MAI, 2012, no. 55, pp. 5. (in Russian)

25. Kopiev V.F., Titarev V.A., Belyaev I.V. Development of a methodology for propeller noise calculation on high-performance computer. TSAGI Science Journal, 2014, vol. 45, no. 3-4, pp. 293– 327. https://doi.org/10.1615/TsAGISciJ.2014011857

26. Costes M., Renaud T., Rodriguez B. Rotorcraft simulations: a challenge for CFD. International Journal of Computational Fluid Dynamics, 2012, vol. 26, no. 6-8, pp. 383–405. https://doi.org/10.1080/10618562.2012.726710

27. Costes M., Renaud T., Rodriguez B., Reboul G. Application of vorticity confinement to rotor wake simulations. International Journal of Engineering Systems, Modelling and Simulation, 2012, vol. 4, no. 1-2, pp. 102–112. https://doi.org/10.1504/ijesms.2012.044848

28. Popov N.I., Emelianova O.V., Jatsun S.F. Modelling of dynamics of flight of a quadrotor helicopter. Vestnik Voronezhskogo instituta GPS MChS Rossii, 2014, no. 4(13), pp. 69–75.

29. Kanatnikov A. N., Akopyan K. R. The plane motion control of the quadrocopter. Mathematics and Mathematical Modelling, 2015, no. 2, pp. 23–36. (in Russian). https://doi.org/10.7463/mathm.0215.0789477

30. Shydakov V.I. Ground effect on aerodynamic characteristics of aerial vehicle with lifted system of shrouded rotor. Trudy MAI, 2011, no. 49, pp. 24. (in Russian)

31. Volkov K. Numerical analysis of Navier-Stokes equations on unstructured meshes. Handbook on Navier-Stokes Equations: Theory and Analysis. Nova Science, 2016, pp. 365–442.

32. Volkov K. Multigrid and preconditioning techniques in CFD applications. CFD Techniques and Thermo-Mechanics Applications. Springer International Publishing, 2018, pp. 83–149. https://doi.org/10.1007/978-3-319-70945-1_6

33. Suvorov A.S., Korotin P.I., Sokov E.M. Finite element method for simulating noise emission generated by inhomogeneities of bodies moving in a turbulent fluid flow. Acoustical Physics, 2018, vol. 64, no. 6, pp. 778–788. https://doi.org/10.1134/S1063771018060106

34. Spalart P.R., Allmaras S.R. A one-equation turbulence model for aerodynamic flows. Proc. of the 30th Aerospace Sciences Meeting and Exhibit, 2992, pp. 1992-0439. https://doi.org/10.2514/6.1992-439

35. Menter F.R. Zonal two-equation k-ω turbulence models for aerodynamic flows. Proc. of the 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference, 1993, pp. 1993-2906. https://doi.org/10.2514/6.1993-2906

36. Menter F.R., Langtry R., Volker S. Transition modelling for general purpose CFD codes. Flow, Turbulence and Combustion, 2006, vol. 77, no. 1-4, pp. 277–303. https://doi.org/10.1007/s10494-006-9047-1